Observations of both Ethernet traffic and variable bit rate (VBR) video traffic
have demonstrated that these traffics exhibit ``self-similarity'' and/or in
finite asymptotic index of dispersion for counts (IDC).
We report here on measurements of traffic in
a commercial public broadband network where similar characteristics
have been observed.
For the purpose of analysis and dimensioning of the central links
of an ATM network we analyse in this paper
the performance of a single server queue fed by Gaussian traffic with
infinite IDC. The analysis leads to an approximation for the performance
of a queue in which
the arriving traffic is ``fractal'' Gaussian and consequently where there
does not exist a dominant negative-exponential tail.
The term ``fractal'' is used here
in the sense that the autocovariance of the traffic exhibits
self-similarity, that is to say, where the autocovariance of
an aggregate of the traffic is the same, or asymptotically the same
for large time lags, as the original traffic.
We are not concerned with proving or
exploiting this self-similarity property as such,
but only with performance analysis techniques which are effective for
such processes. In order to be able to test the performance
analysis formulae, we show that traffic with the same autocovariance
as measured in a real network over a wide range of lags (sufficiently
wide a range for the traffic to be equivalent from
the point of view of queueing performance) can be generated as
a mixture of two Gaussian AR(1) processes.
In this way we demonstrate that the analytic performance formulae
are accurate.